Instructions: Answer the following questions on a separate sheet of paper. Show all of your work as illustrated in the example shown below. Some of the problems may seem simple or intuitive, but work must be shown for credit.

Example: You are watching workers along a railroad strike a railroad tie that holds the tracks together. The workers swing with a constant rhythm so that you hear 14 strikes over one minute (60 sec) of time.

What is the frequency of the workers' swings?

What is their period?

1. A wave hits a pylon of a pier every 2.7 seconds. What is the frequency of the waves?

2. A pendulum swings back and forth 27 times in 35.2 sec. What is the period of the pendulum?

What is this pendulum's frequency?

3. A jack hammer has a frequency of 37 hz; that is, it vibrates 37 times a second in order to break up concrete and other material. How long does it take to vibrate one time; that is, what is its period?

4. A police officer observes cars traveling down a highway. He counts 78 cars pass by him every minute. What is the frequency of the cars in hertz?

On average, how many seconds must the police office wait between cars?

5. A mass attached to a spring vibrates up and down with a frequency of 1.7 hertz. How much time would be required for it to complete 33 vibrations?

6. The A-string on a guitar vibrates back and forth at a frequency of 220 hertz. How many seconds does it take the string to move from its lowest position to its highest position? Be careful and take into account how much of a vibration passes as the string vibrates between it lowest to highest position.

7. An electron orbits a nucleus with a period of 23.1 x 10-9 seconds, or 23.1 nanoseconds. What is the frequency of the electron’s oscillations?

How many orbits would an electron make in one full second?

8. A group of children are playing jump rope. Each child stays in the middle for 2 minutes. If the frequency the children are spinning the rope is 0.76 hertz. How many times will a child need to jump while in the middle?